Question

A solid ball of mass m and radius r is given linear velocity v and no angular velocity and placed on a rough surface. What is the velocity of centre of mass when ball starts pure rolling

Answer 1

The velocity of centre of mass is  v' = 5/7 v

Explanation:

mvcr + Iω = mvr

When pure rolling starts.

ω = v / r

mvcr + 2/5 mr^2  x v /r = mvr

v = v' + 2/5 v'

v = 7/5 v'

v' = 5/7 v

Thus the velocity of centre of mass is  v' = 5/7 v

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